Girls and women with Turner syndrome between the ages of 14 and 50 years may be eligible for this 2-year study. Three months before beginning treatment, all patients will wear an estrogen patch and take a progesterone tablet daily for 10 days each month. They will then be randomly assigned to one of two treatment groups to compare the effects of estrogen alone with estrogen plus testosterone on bone strength, muscle and fat mass and psychosocial well being. Both groups will wear an estrogen patch and take oral progesterone. One group will also wear a testosterone patch while the other group will wear a placebo patch (a patch that does not contain any testosterone). Neither study participants nor the doctors will know who is getting the testosterone until the study is complete. Patients will undergo the following procedures before beginning treatment and at 6, 12 and 24 months after starting treatment: